Process and device for monitoring the cross-sectional profile of a continuously produced web of material

ABSTRACT

A predetermined number of actuators are arranged transversally to a continuously produced material web for adjusting the cross-sectional profile of the web. To determine to what degree the instantaneous cross-sectional profile can approximate a reference profile, an optimally achievable profile is determined first in a computing device on the basis of a measured profile and a mathematical model of a controlled system of a cross-sectional profile control, and the optimally achievable profile is compared with the measured profile.

FIELD OF THE INVENTION

The present invention relates to a method and a device for monitoringthe cross-sectional profile of a continuously produced web of material.

BACKGROUND INFORMATION

In many processes where continuous webs of material are produced, it isof interest to provide products such as, for example, paper webs orfoils with the most uniform possible characteristics; thus, theseproducts should be homogenous and of a consistent quality. To obtain therelevant material characteristics, e.g., thickness, specific weight, ormoisture content (having a numerical representation), thecharacteristics are measured in the longitudinal and transversaldirections of the web of material and are represented as a profile inthese directions. The cross-sectional profile is normally obtainedbroken down into a number of measured values, where the profile isaverage-free or is made average-free. It is desirable for the measuredprofile to correspond to a predefined reference profile, the referenceprofile is often being a zero. To achieve the desired correspondence, apredefined number of actuators, driven by a control system as a functionof the system deviation between the given reference profile and themeasured profile, is placed transversally to the material web.

An apparatus having a control device in which the actual cross-sectionalprofile control is optimized, is shown in U.S. Pat. No. 5,170,357.

It is possible that a cross-sectional profile cannot be given alldesired shapes with a finite number of actuators. In particular,absolute smoothness cannot be achieved. Accordingly, it is questionableas to what extent the reference profile can be approximated bycontrolling the cross-sectional profile.

An article, R. Munch, "Der JETCOmmander--ein fortschrittliches Systemzur Fernverstellung der Stoffauflaufblende und zur Regelung desFlachengewicht-Querprofils" (The JETCOmmander--an advanced system forremote adjustment of the material winding aperture and control of thesurface weight cross-sectional profile) Wockenblatt fuerPapierfabrikation 7, 1992, pp. 259-265, illustrates a process forestimating the improvement potential when a surface weightcross-sectional profile on a papermaking machine is controlled, wherethe variance of the measured profile is broken down into its wavelengthcomponents from which the improvement potential of the measured profileis estimated. In such a process, the accuracy of the estimate is limitedsince the optimum achievable profile is unknown.

In contrast, the object of the present invention is to provide a processand design means to improve the evaluation of the control devices forcross-sectional profiles of continuously produced material webs.

SUMMARY OF THE INVENTION

The present invention relates to a method and a device, wherein theoptimally achievable profile is calculated in a computing device as afunction of the measured profile and a mathematical model of thecontrolled system and made available for comparison with the measuredprofile for cross-sectional profile control with a control device, towhose input the system deviation between a predefined reference profileand the measured profile are supplied, and which actuates, at itsoutput, a predefined number of actuators as a function of the systemdeviation to adjust the profile of the material web.

An advantage of the method and device according to the present inventionconsists of determining the actually desired, optimally achievable,profile first, where the profile is not constant and is dependent on theprofile measurements. By comparing to the measured profile, a highlygraphic evaluation tool is provided for estimating the possible profileimprovement.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of a device for executing the methodaccording to the present invention.

FIG. 2 shows a structure of a control circuit for controllingcross-sectional profiles as shown in FIG. 1 according to the presentinvention.

FIGS. 3-6 show possible representations of measured and correspondingoptimum achievable profiles determined by the method and the device ofthe present invention.

FIGS. 7-10 show the Fourier spectra of the profiles as illustrated inFIGS. 3-6.

FIG. 11 shows a limit curve illustrating an optimum profile which may beobtained in the worst-case scenario according to the present invention.

DETAILED DESCRIPTION

FIG. 1 shows a device for controlling the cross-sectional profile of acontinuously produced material web 1, where the process to be controlled(obtaining a predefined cross-sectional profile) takes place in thedirection of arrow 2. To adjust the cross-sectional profile of materialweb 1, a predefined number of n actuators 3 are arranged preferablyevenly spaced over the entire width of material web 1. As shown indirection 2 of the process flow, another m number of sensors 4, whichsense the cross-sectional profile of material web 1 which are brokendown into m measured values, are arranged behind actuators 3. Acomputing device 5, consisting of a digital computer with RAM, programstorage, and data storage devices, is used for controlling thecross-sectional profile of material web 1. An interface module 6 isprovided between computing device 5 and the process. Computing device 5generates control commands for actuators 3 according to the controlprogram ran by the computing device 5 whose commands are supplied toactuators 3 through interface module 6. The control commands foractuators 3 are generated as a function of the system deviation betweenthe actual profile y_(act) measured by sensors 4 (and supplied tocomputing device 5 through interface module 6) and a predefinedreference profile y_(ref). y_(ref) is supplied to computing device 5through an input/output unit 7, through which computing device 5communicates with the outside world. Furthermore, a display device 8 fordisplaying the process parameters is connected to computing device 5.Computing device 5 is also connected to a separate device 9, which iseither another computing device or a program designed to be run incomputing device 5 to execute the procedure according to the presentinvention.

FIG. 2 shows a structure of the cross-sectional profile control circuitshown in FIG. 1. This control circuit consists of a control device 10and a controlled system 11. Control device 10 is implemented as aprogram running in computing device 5, and controlled system 11 isformed by the process to be controlled, (e.g., the adjustment of thecross-sectional profile of material web 1). Control device 10 generatescontrol parameters which act on the process through actuators 3 or thecontrol profile u from the system deviation e between the referenceprofile y_(ref) and the measured actual profile y_(act). According tothe characteristics of the process to be controlled, the initial profiley is formed from control profile u in the controlled system 11. Themeasured actual profile y_(act) consists of the initial profile y and aprocess-specific error profile y_(err). Depending on the number m ofsensors 4, the actual profile y_(act) reference profile y_(ref), errorprofile y_(err), initial profile y and system deviation e are formedusing an m-dimensional vector with m parameters. Control profile u isrepresented in the form of an n-dimensional vector combining the controlparameters for the n actuators 3. Assuming that the process to becontrolled includes a linear characteristic, the static component shallonly be discussed, (i.e., the mxn transfer matrix P formed by initialprofile y from control profile u, with y=Pu).

It is possible that a cross-sectional profile y may not be given alldesired shapes with a finite number n of actuators 3. To estimate thepotential for improvement of the cross-sectional profile control, firstthe optimum achievable profile (the profile with the smallest varianceσ² and therefore the smallest standard deviation σ) is calculated firstin unit 9 for the predefined reference profile y_(ref) and for aprocess-specific error profile y_(err). Normally, in practice, variance2σ is used as the quality criterion for the adjusted profile.

The m-dimensional profile of the system deviation is as follows:

    e=y.sub.ref -(Pu+y.sub.err).

Accordingly, the variance is:

    σ.sup.2 =e.sup.T e=(y.sub.ref -Pu-y.sub.err).sup.T (y.sub.ref -Pu-y.sub.err)

and thus the standard deviation σ is minimized using u.

A minimum variance σ² is obtained when:

    δσ.sup.2 /δu=-2P.sup.T (y.sub.ref -y.sub.err)+2P.sup.T Pu.sub.opt =0.

Accordingly, the following result is obtained:

    u.sub.opt =(P.sup.T P).sup.-1 P.sup.T (y.sub.ref -y.sub.err).

Thus, for the optimum profile e_(opt), we obtain:

    e.sub.opt =(I-(P.sup.T P).sup.-1 P.sup.T) (y.sub.ref -y.sub.err)

with the mxn unit matrix I and the pseudo-inverse

    P.sup.0 =(P.sup.T P).sup.-1 P.sup.T.

Denoting

    y.sub.err =y.sub.act -Pu,

error profile y_(err) is obtained and the smallest possible systemdeviation achievable in the optimum case is:

    e.sub.opt =(I-P(P.sup.T P).sup.-1 P.sup.T) (y.sub.ref -y.sub.act).

With the method and the device according to the present invention, thebest possible cross-sectional profile, i.e., the profile with thesmallest possible variance or standard deviation, is obtained in unit 9for a given reference profile y_(ref) directly from the measured actualprofile y_(act) The optimum profile e_(opt) of the system deviation issupplied to display device 8 together with the instantaneous profile ofthe system deviation e=y_(ref) -y_(act) where it is representedgraphically. The direct graphic comparison between the optimum profilee_(opt) and the instantaneous control error profile e makes it possibleto evaluate the improvement potential still available. It can also beused for demonstrating that a profile can no longer be improved, or thata certain jaggedness in the measured profile can no longer bediminished. Of course, such a comparison between the optimum profilee_(opt) and the instantaneous control error profile e can also be madeautomatically in unit 9 or computing device 5.

FIG. 3 shows, using an example of the cross-sectional profile control ofa papermaking machine, where the surface weight cross-sectional profileis measured prior to the beginning of the control. The correspondingoptimum profile calculated in unit 9 is shown in FIG. 4. FIG. 5 showsthe measured cross-sectional profile after starting the cross-sectionalprofile control, and FIG. 6 again shows the corresponding optimumprofile. The diagrams are plotted in g/m² against measured parameters. Acomparison of FIGS. 3 and 4 shows that prior to starting thecross-sectional profile control, there is still an improvement potentialof 58%, while (as shown by a comparison of FIGS. 5 and 6) theimprovement potential dropped to 14% after starting the control; thismeans that the actual profile corresponds to optimum achievable profileto a degree of 86%.

In principle, profile components with a lower frequency (components witha considerably greater wavelength than the distance between two adjacentactuators 3) may be properly adjusted, while higher-frequency componentsare adjusted poorly or not at all. To obtain information regarding towhat extent the individual spectral components of the cross-sectionalprofile can be improved through control in the optimum case, the Fouriertransforms E and E_(opt) of the measured profiles of the systemdeviation e and the optimum profile e_(opt) are determined in unit 9,using a transformation matrix T with the elements

    t.sub.ki =exp(-j2nki/m), where i,k=0,1, . . . , m-1;

    E=Te

    E.sub.opt =Te.sub.opt =T(I-P(P.sup.T P).sup.-1 P.sup.T)T.sup.-1 E.

The improvement potential of the cross-sectional profile is determinedusing the profile spectra E and E_(opt) in the same manner, as wasexplained above for profiles e and e_(opt). FIGS. 7 through 10illustrate such improvement using a spectra corresponding to theprofiles of FIGS. 3-6. In FIGS. 3-6, the amplitudes |E_(k) | of theindividual spectral components E_(k) are plotted against theirwavelengths

    λ.sub.k =n/k,

where the wavelengths η_(k) of the individual spectral components E_(k)are plotted as multiples of a distance between actuators. In particular,FIG. 7 shows spectrum E of the measured profile e prior to control, FIG.8 shows spectrum E_(opt) of the corresponding optimum profile e_(opt),FIG. 9 shows spectrum E of the measured adjusted profile e, and FIG. 10shows spectrum E_(opt) of the corresponding optimum profile e_(opt). Ascan be seen from FIGS. 7 through 10, the greatest improvement in theprofile is achieved in the long-wavelength area.

As illustrated above, for each error profile y_(err) or measure profiley_(act) there is a corresponding special optimum profile e_(opt). Eachof the optimum profiles e_(opt) also includes an individual spectraldistribution E_(opt) from which it can be seen how large are amplitudes|E_(opt),k | of the individual wavelengths η_(k). Different spectraldistributions E_(opt) of the optimum profiles usually result indifferent amplitude values |E_(opt),k |. One of the important parametersis the highest possible value of |E_(opt),k |, e.g., its upper limitη_(k). This value illustrates how bad the optimum solution forwavelength λ_(k) can be in the worst case or how good it must be as aminimum. The limit η_(k) shows the minimum factor by which the amplitude|E_(k) | of an error in the wavelength λ_(k) can be reduced. The limitη_(k) is calculated in unit 9, accordingly:

    η.sub.k =max |E.sub.opt,k |=(1-1/m||P(P.sup.T P).sup.-1 P.sup.T tk||.sub.2.sup.2).sup.1/2.

    ||E||.sub.2 =1

where t_(k) denotes the kth column vector of transformation matrix T.The limit values η_(k) together form the limit curve

    η.sup.T =(η.sub.0, n.sub.1, . . . , η.sub.m-1),

which is not dependent on the individual profiles, but only oncharacteristic P of the controlled system 11. If characteristic P isconstant, the limit curve η can be determined only once. On the otherhand, if P varies, for example, as a function of the process status, thelimit curve η must, in general, be determined again. FIG. 11 shows anexample of limit curve q as a function of the wavelengths λ_(k), whichare shown as multiples of the distance between actuators. It can beclearly seen that hardly any improvement can be achieved for wavelengthsλ_(k) smaller than twice the distance between actuators.

I claim:
 1. A method for monitoring a cross-sectional profile of amaterial web continuously produced with a controlled systemcharacterized by a model, the method comprising the steps of:obtaining ameasured profile of the material web; determining a control deviationbetween a predetermined reference profile and the measured profile;actuating at least one actuator as a function of the control deviationfor adjusting the cross-sectional profile of the material web;calculating an optimally achievable profile as a function of themeasured profile using the model of the controlled system; and comparingthe optimally achievable profile and the measured profile.
 2. The methodaccording to claim 1, wherein the step of calculating the optimallyachievable profile includes calculating a minimum achievable systemdeviation e_(opt) so that:e_(opt) =(I-P(P^(t) P)⁻¹ P^(T))(y_(ref)-y_(act)), wherein:y_(ref) represents the predetermined referenceprofile, y_(act) represents the measured profile, P is a transfer matrixof the controlled system for determining the cross-sectional profile yof the material web from control parameters u of the actuators, so thaty=Pu, P^(T) is a transposed matrix of the matrix P, and I is a unitmatrix.
 3. The method according to claim 1, wherein the step ofcalculating the optimally achievable profile includes calculating aFourier transform E_(opt) of a minimum achievable system deviation sothat:E_(opt) =T I-P(P^(T) P)⁻¹ P^(T) !T⁻¹ E, wherein:P is a transfermatrix of the controlled system for determining the cross-sectionalprofile y of the material web from control parameters u of theactuators, so that y=Pu, P^(T) is a transposed matrix of the matrix P, Iis a unit matrix, and T is a transformation matrix for a Fouriertransformation.
 4. The method according to claim 3, further comprisingthe step of:calculating limit values η_(k) so that:η_(k)=(1-1/m||P(P^(T) P)⁻¹ P^(T) t_(k) ||₂ ²)^(1/2), the limit values η_(k)representing a spectral limit curve η^(T) so that:η^(T) =(η₀, η₁, . . ., η_(m-1)), wherein the spectral limit curve η^(T) provides the largestamplitudes of a Fourier spectrum of the minimum achievable controldeviation independently of the control deviation, and wherein m is anumber of column vectors and t_(k) is a kth column vector of thetransformation matrix T.
 5. The method according to claim 1 includingthe step of displaying at least one of the measured profile, the optimumachievable profile, a Fourier transform of the measured profile and aFourier transform of the optimum achievable profile.
 6. A device formonitoring a cross-sectional profile of a continuously produced materialweb continuously produced with a controlled system characterized by amodel, comprising:a measuring device for obtaining a measured profile ofthe material web; means for determining a control deviation between apredetermined reference profile and the measured profile; a controldevice including a control input and an output, the control inputreceiving the control deviation; at least one actuator coupled to theoutput of the control device, the control device controlling the atleast one actuator as a function of the control deviation for adjustingthe cross-sectional profile of the material web; a computing device forcalculating an optimum achievable profile as a function of the measuredprofile using the model of the controlled system; and means forcomparing the optimally achievable profile and the measured profile. 7.The device according to claim 6, wherein the computing device calculatesthe optimally achievable profile by calculating a minimum achievablesystem deviation e_(opt) so that:e_(opt) =(I-P(P^(T) P)⁻¹ P^(T))(y_(ref)-y_(act)), wherein:y_(ref) represents the predetermined referenceprofile, y_(act) represents the measured profile, P is a transfer matrixof the controlled system for determining the cross-sectional profile yof the material web from control parameters u of the actuators, so thaty=Pu, P^(T) is a transposed matrix of the matrix P, and I is a unitmatrix.
 8. The system according to claim 6, wherein the computing devicecalculates the optimally achievable profile by calculating a Fouriertransform E_(opt) of a minimum achievable system deviation sothat:E_(opt) =T I-P(P^(T) P)⁻¹ P^(T) !T⁻¹ E, wherein:P is a transfermatrix of the controlled system for determining the cross-sectionalprofile y of the material web from control parameters u of theactuators, so that y=Pu, P^(T) is a transposed matrix of the matrix P, Iis a unit matrix, and T is a transformation matrix for a Fouriertransformation.
 9. The system according to claim 8, wherein thecomputing device calculates limit values η_(k) so that:η_(k)=(1-1/m||P(P^(T) P)⁻¹ P^(T) t_(k) ||₂ ²)^(1/2), the limit values η_(k)representing a spectral limit curve η^(T) so that:η^(T) =(η₀, η₁, . . ., η_(m-1)), wherein the spectral limit curve η^(T) provides the largestamplitudes of a Fourier spectrum of the minimum achievable controldeviation independently of the control deviation, and wherein m is anumber of column vectors and t_(k) is a kth column vector of thetransformation matrix T.
 10. The device according to claim 6, furthercomprising:a displaying device for displaying at least one of themeasured profile, the optimum achievable profile, a Fourier transform ofthe measured profile and a Fourier transform of the optimum achievableprofile.